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Lecturer
Serena Cenatiempo serena.cenatiempo@gssi.it
Timetable and workload
Lectures: 16 hours
Period: September/October 2026.
Course Description
Quantum statistical mechanics studies quantum systems composed of a large number of particles, with the aim of understanding their macroscopic behavior starting from their fundamental microscopic description. While in the absence of interactions the properties of many-body systems can be deduced from the single-particle Hamiltonian, the analysis of their evolution and thermodynamic properties becomes significantly more complex when interactions are present. In many situations, however, it is sufficient to obtain an effective description of the many-body system—providing an approximation of its evolution or equilibrium properties in certain regimes and/or up to specific time scales.
In this course, we will focus on a paradigmatic phenomenon in which collective macroscopic behavior emerges from a many-body system: Bose–Einstein condensation. We will discuss how the nonlinear Hartree and Gross–Pitaevskii equations arise as effective descriptions for the dynamics of a large number of particles exhibiting condensation. Time permitting, we will also address static problems and explain how quantum fluctuations around the condensate can be accurately described by the so-called Bogoliubov theory in relevant scaling regimes.
Course requirement
Basic elements of the theory of linear operators in Hilbert spaces.
The knowledge of the formalism Quantum Mechanics may be helpful.
Connections with other courses
Introduction to the non linear Schrödinger Equation
Dynamics of Open Quantum Systems